GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A theoretical comparison of the Arnoldi and GMRES algorithms
SIAM Journal on Scientific and Statistical Computing
Stopping criteria for iterative solvers
SIAM Journal on Matrix Analysis and Applications
Relations Between Galerkin and Norm-Minimizing Iterative Methodsfor Solving Linear Systems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Error Analysis of Krylov Methods In a Nutshell
SIAM Journal on Scientific Computing
Error Estimates for the Solution of Linear Systems
SIAM Journal on Scientific Computing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
SIAM Journal on Matrix Analysis and Applications
The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments, and Tools)
Matrices, Moments and Quadrature with Applications
Matrices, Moments and Quadrature with Applications
| Hi-index | 0.00 |
We provide formulas for the norm of the error when solving nonsymmetric linear systems with the full orthogonalization method (FOM) and the generalized minimum residual method (GMRES) as well as relations between the error norm and the residual norm. From these formulas we are able to compute estimates of the norm of the error during the iterations. Since stopping criteria based on the norm of the residual may sometimes be misleading, such estimates could lead to a more robust way to stop the iterations. Numerical experiments show that the proposed norm estimates work nicely on difficult linear systems.